Hyperbolic groups, Cannon-Thurston maps, and hydra

Members' Seminar
Topic:Hyperbolic groups, Cannon-Thurston maps, and hydra
Speaker:Timothy Riley
Affiliation:Cornell University; Member, School of Mathematics
Date:Monday, November 17
Time/Room:2:00pm - 3:00pm/S-101
Video Link:http://video.ias.edu/membersem/2014/1117-TimothyRiley

Groups are Gromov-hyperbolic when all geodesic triangles in their Cayley graphs are close to being tripods. Despite being tree-like in this manner, they can harbour extreme wildness in their subgroups. I will describe examples stemming from a re-imagining of Hercules' battle with the hydra, where wildness is found in properties of "Cannon-Thurston maps" between boundaries. Also, I will give examples where this map between boundaries fails to be defined. This is joint work with O. Baker.